Dance Of The Spaghetti

Classical Mechanics Level 5

When we cook spaghetti, noodles loosen up as they take on water, and undergo a beautiful choreography driven by the thermal energy of the boiling water. Although they become more flexible, they still maintain some structure, i.e. they are smooth curves.

We can make a crude model of the spaghetti noodle as a chain of \(N\) short rods of length \(\delta l\) that are connected end to end, but otherwise free to rotate about the connections. Under these assumptions, calculate the root mean squared distance (in \(\si{\centi\meter}\)) between the ends of the noodle (i.e. the blue and red balls in the diagram) as it dances in the pot.

Details and Assumptions:

  • \(\delta l = 1 \si{\milli\meter}\).
  • \(N = 350\).
  • Ignore the nasty issue of the fact that spaghetti cannot pass through itself.
  • Assume the spaghetti is alone in the pot ‚Äčand doesn't interact with the walls.

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